Mixing Rates for a Random Walk on the Cube

1987 ◽  
Vol 8 (4) ◽  
pp. 746-752 ◽  
Author(s):  
Peter Matthews
Keyword(s):  
Random Walk ◽  
Mixing Rates

scholarly journals NON-BACKTRACKING RANDOM WALKS MIX FASTER

2007 ◽  
Vol 09 (04) ◽  
pp. 585-603 ◽  
Author(s):  
NOGA ALON ◽  
ITAI BENJAMINI ◽  
EYAL LUBETZKY ◽  
SASHA SODIN
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Chebyshev Polynomials ◽  
Simple Random Walk ◽  
Mixing Rate ◽  
Ramanujan Graph ◽  
Mixing Rates

We compute the mixing rate of a non-backtracking random walk on a regular expander. Using some properties of Chebyshev polynomials of the second kind, we show that this rate may be up to twice as fast as the mixing rate of the simple random walk. The closer the expander is to a Ramanujan graph, the higher the ratio between the above two mixing rates is. As an application, we show that if G is a high-girth regular expander on n vertices, then a typical non-backtracking random walk of length n on G does not visit a vertex more than [Formula: see text] times, and this result is tight. In this sense, the multi-set of visited vertices is analogous to the result of throwing n balls to n bins uniformly, in contrast to the simple random walk on G, which almost surely visits some vertex Ω( log n) times.

Elements of the Random Walk

2004 ◽  
Author(s):  
Joseph Rudnick ◽  
George Gaspari
Keyword(s):  
Random Walk

CUBIC [001] TWIST CSL GRAIN BOUNDARIES STUDY BY MEANS OF RANDOM WALK

1990 ◽  
Vol 51 (C1) ◽  
pp. C1-67-C1-69
Author(s):  
P. ARGYRAKIS ◽  
E. G. DONI ◽  
TH. SARIKOUDIS ◽  
A. HAIRIE ◽  
G. L. BLERIS
Keyword(s):  
Random Walk ◽  
Grain Boundaries

Random walk to graphene

2011 ◽  
Vol 181 (12) ◽  
pp. 1284 ◽  
Author(s):  
Andrei K. Geim
Keyword(s):  
Random Walk
Sign in / Sign up

Export Citation Format

Share Document